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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    The probability of choosing randomly a number\[c\]from the set\[\{1,\,\,2,\,\,3,...,\,\,9\}\]such that the quadratic equation\[{{x}^{2}}+4x+c=0\]has real roots is

    A) \[\frac{1}{9}\]                                   

    B) \[\frac{2}{9}\]

    C) \[\frac{3}{9}\]                   

    D)        \[\frac{4}{9}\]

    Correct Answer: D

    Solution :

    Given,\[{{x}^{2}}+4x+c=0\] For real roots,                 \[D={{b}^{2}}-4ac\ge 0\]                 \[=16-4c\ge 0\] \[\Rightarrow \,\,c=1,\,\,2,\,\,3,\,\,4\]will satisfy  the  above inequality. \[\therefore \]Required probability\[=\frac{4}{9}\]


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